The "Here's where Brian goes berserk" cutaway is a parody of the "Here's where Cameron goes berserk" scene. Rolling the "odometer" back is also a key scene in Ferris Bueller's Day Off, in which the odometer of a car was rolled back to conceal that it had been driven.
When Brian tries to reprogram Stewie's time machine it displays an avatar of Stewie saying "Uh, uh, uh," just like Dennis Nedry's computer system in Jurassic Park.